Consider the linear control system whose state-space equations aredx/dl = Ax + Bu,y = Cx + Duwherex,uandyare, respectively, the state, input and output vectors, andA, B, C, Dare constant matrices. Problem : find constant scalarsrand constant vectorsv, wsuch that an input of the formvexp(rt)1(t)will yield a state of the formx = wexp(rt)and outputy≡ 0,t≥ 0. The method developed is this: the output equation is solved for x and the solution is substituted into the state equation. The resulting equation must satisfy a consistency condition involvingr, in order for a solution of the problem to exist. Matrix generalized inverses are employed both to derive consistency conditions and to obtain solutions. Several examples illustrate a variety of conditions.